Problem: Solve for $x$ and $y$ using elimination. ${-2x+3y = 8}$ ${-5x-y = -14}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the bottom equation by $3$ ${-2x+3y = 8}$ $-15x-3y = -42$ Add the top and bottom equations together. $-17x = -34$ $\dfrac{-17x}{{-17}} = \dfrac{-34}{{-17}}$ ${x = 2}$ Now that you know ${x = 2}$ , plug it back into $\thinspace {-2x+3y = 8}\thinspace$ to find $y$ ${-2}{(2)}{ + 3y = 8}$ $-4+3y = 8$ $-4{+4} + 3y = 8{+4}$ $3y = 12$ $\dfrac{3y}{{3}} = \dfrac{12}{{3}}$ ${y = 4}$ You can also plug ${x = 2}$ into $\thinspace {-5x-y = -14}\thinspace$ and get the same answer for $y$ : ${-5}{(2)}{ - y = -14}$ ${y = 4}$